OBLIQUE DUAL FRAMES IN FINITE-DIMENSIONAL HILBERT SPACES

National Natural Science Foundation of China [61170324]; TianYuan Special Funds of the National Natural Science Foundation of China [11226099]; Natural Science Foundation of Fujian Province, China [2012J01005]; Fuzhou University, China [2012-XQ-29, 2012-XY-21]; Scientific Research Start-up Foundation of Fuzhou University, China [022410]A frame can be completed to a tight frame by adding some additional vectors. However, for the purpose of computational efficiency, we need to put restrictions to the number of added vectors. In this paper we propose a constructive method that allows to extend a given frame to an oblique dual frame pair such that the number of added vectors is in general much smaller than the number of added vectors used to extend it to a tight frame. We also present a uniqueness characterization and several equivalent characterizations for an oblique dual frame pair, it turns out that oblique dual frame pair provides more flexibilities than alternate dual frame pair